After graduating from USC with a degree in education, Kate took a job as an artist at Clemson University. At Clemson, she met Jim Palmer, a faculty member in the agronomy department. Jim and Kate were married in 1970. Kate taught sixth grade for a year in Seneca, and the next year she taught art in Pickens. After bringing two children into the world—James (in 1971) and Salley in 1974)—Kate began drawing political cartoons for the Greenville News, and in 1978 she became the first full-time editorial cartoonist in South Carolina. While a cartoonist at the News, Kate became one of three women members of the American Association of Editorial Cartoonists, won the National Freedom Foundation's Principal Award for Editorial Cartoonists, and was syndicated nationally in over 200 newspapers by News America Syndicate. Her cartoons have appeared in the New York Times, the Washington Post, and many other national outlets, including Newsweek Magazine and CBS's Face the Nation. In 1984, Kate resigned from the Greenville News and freelanced for other state newspapers while remaining nationally syndicated until 1987.

In 1990, Kate illustrated her first picture book, How Many Feet in the Bed?, which was written by Diane Johnston Hamm and published by Simon and Schuster. Later that same year, Simon and Schuster published A Gracious Plenty, a book Kate wrote and illustrated about her great aunt May Zeigler in Orangeburg. In 1992, Kate illustrated Octopus Hug, written by Lawrence Pringle and published by Boyds Mills Press.

Throughout the 1990s, Kate illustrated more than two dozen books, including a number of Reading Recovery books for children (written by various authors and published by the Kaeden Corporation). In addition, Kate started a syndicated fax caricature service for newspapers called "Just the Fax!" and contributed several freelance op-ed columns for various newspapers, addressing such burning issues of the times as the Susan Smith trial (Newsday) and the O. J. Simpson verdict (the State).

In the fall of 1998, Kate and Jim founded Warbranch Press, Inc., to publish and sell Kate's books. They are kept busy developing new book ideas, selling books, and traveling around the region attending professional conferences and other events. Kate makes many public appearances, speaking about her work to school groups and other gatherings of interested individuals.

In 2004, frustrated that many of the children she spoke to in her school visits were unfamiliar with the story of the palmetto tree and its importance to South Carolina, Kate wrote and illustrated Palmetto: Symbol of Courage. That project, which tells the story of the Revolutionary War battle that made the palmetto South Carolina's state tree, has sparked other forays into state and national history, notably Francis Marion and the Legend of the Swamp Fox (illustrated by Kate and Jim's son, James H. Palmer, Jr.) and the forthcoming Black Heroes of the Revolution. Kate also recently completed a memoir of her early life and cartooning career, Growing Up Cartoonist in the Baby-Boom South: A Memoir and Cartoon Retrospective, a work twenty years in the making that was published in 2005 by Clemson University Digital Press.

Kate continues to enjoy writing, illustrating, drawing funny pictures of famous people, and talking to various groups about political cartooning and/or writing and illustrating picture books.